Question 3 of 10
What is i^30?
O A. -1
B. -1
C. i
O D. 1
SUB

-1

Step-by-step explanation:

Rewrite

as

Factor out

Rewrite as

Rewrite as

Rewrite as

Rewrite as

Raise -1 to the power of 2.

One to any power is one.

Multiply  by 1.

Rewrite as -1

[RevyBreeze]

1. -9p - 17 = 10

-9p = 10 + 17

-9p = 27

p = -3

2. w/4 - 4 = 3

w/4 =  3 + 4

w/4 = 7

w = 7 · 4

w = 28

3. x/5 + 6 = 10

x/5 = 10 - 6

x/5 = 4

x = 4 · 5

x = 20

4. -2(m - 30) = -6m

-2m + 60 = -6m

-2m + 6m = -60

4m = -60

m = -15

5. 3.75 + 3.7 = 1.7 + 1.75x

1.75x = 3.75 + 3.7 - 1.7

1.75x = 5.75

x = 23/7

6. -6 - 7(c + 10)

= -6 -7c - 70

= -76 - 7c

7. 2x + 3(x - 2) - 2(x - 6)

= 2x + 3x - 6 - 2x + 12

= 3x + 6

8. c + 6 -3

= c + 3

10. -5p > -30

p < 6

13.  29 - 5x = 4; $5.00

14. 64 + w = 2w + 8; 56 pounds

For Q#5, 7, 8, and 10, I got a different answer from the one you provided. I did it the way I was taught to do it, which might be different from what you were taught. Sorry about that; I tried my best.

1. -9p - 17 = 10

-9p = 10 + 17

-9p = 27

p = -3

2. w/4 - 4 = 3

w/4 =  3 + 4

w/4 = 7

w = 7 · 4

w = 28

3. x/5 + 6 = 10

x/5 = 10 - 6

x/5 = 4

x = 4 · 5

x = 20

4. -2(m - 30) = -6m

-2m + 60 = -6m

-2m + 6m = -60

4m = -60

m = -15

5. 3.75 + 3.7 = 1.7 + 1.75x

1.75x = 3.75 + 3.7 - 1.7

1.75x = 5.75

x = 23/7

6. -6 - 7(c + 10)

= -6 -7c - 70

= -76 - 7c

7. 2x + 3(x - 2) - 2(x - 6)

= 2x + 3x - 6 - 2x + 12

= 3x + 6

8. c + 6 -3

= c + 3

10. -5p > -30

p < 6

13.  29 - 5x = 4; $5.00

14. 64 + w = 2w + 8; 56 pounds

For Q#5, 7, 8, and 10, I got a different answer from the one you provided. I did it the way I was taught to do it, which might be different from what you were taught. Sorry about that; I tried my best.

The answers are as follows:

Step-by-step explanation:

Let us look at the statements one by one

1. The additive inverse of 10 is -10.

The additive inverse of a number is the opposite of a number with respect to sign.

The sum of a number and its additive inverse is zero.

This statement is true.

2. Zero is a positive number.

Zero is neither a positive number nor a negative number. It is only used as reference to decide whether a number is positive or negative.

This statement is false.

3. To divide two unlike signs, the quotient is always positive.

When two unlike signs are divided, the answer will be negative as division involves multiplication, and multiplication of two numbers with unlike signs will always be negative.

This statement is false.

4. Commutative Property states that:

a + (b + c ) = (a + b ) + c

Commutative property deals with two numbers or variables only. The property with three numbers or varibales is associative property. Hence,

This statement is false.

5. One is the identity element of for addition.

Additive identity is a number that when added to a number x, the result will always be x. Zero is additive identity.

Hence,

This statement is false.

The answers are as follows:

The answers are as follows:

Step-by-step explanation:

Let us look at the statements one by one

1. The additive inverse of 10 is -10.

The additive inverse of a number is the opposite of a number with respect to sign.

The sum of a number and its additive inverse is zero.

This statement is true.

2. Zero is a positive number.

Zero is neither a positive number nor a negative number. It is only used as reference to decide whether a number is positive or negative.

This statement is false.

3. To divide two unlike signs, the quotient is always positive.

When two unlike signs are divided, the answer will be negative as division involves multiplication, and multiplication of two numbers with unlike signs will always be negative.

This statement is false.

4. Commutative Property states that:

a + (b + c ) = (a + b ) + c

Commutative property deals with two numbers or variables only. The property with three numbers or varibales is associative property. Hence,

This statement is false.

5. One is the identity element of for addition.

Additive identity is a number that when added to a number x, the result will always be x. Zero is additive identity.

Hence,

This statement is false.

The answers are as follows:

c. 6,3x10⁻¹¹M

Explanation:

The solubility of a buffer is defined as the concentration of the dissolved solid in a saturated solution. For the Cd(OH)₂, solubility is:

[Cd²⁺] = S

The dissolution of Cd(OH)₂ is:

Cd(OH)₂ ⇄ Cd²⁺ + 2OH⁻

And the ksp is defined as:

ksp = [Cd²⁺][OH⁻]²

As ksp = 2,5x10⁻¹⁴ and [OH⁻] at pH=12,30 = 10^-(14-12,30) = 0,01995M

2,5x10⁻¹⁴ = [Cd²⁺]×(0,01995M)²

[Cd²⁺] = 6,3x10⁻¹¹M

That means solubility is c. 6,3x10⁻¹¹M

I hope it helps!

c. 6,3x10⁻¹¹M

Explanation:

The solubility of a buffer is defined as the concentration of the dissolved solid in a saturated solution. For the Cd(OH)₂, solubility is:

[Cd²⁺] = S

The dissolution of Cd(OH)₂ is:

Cd(OH)₂ ⇄ Cd²⁺ + 2OH⁻

And the ksp is defined as:

ksp = [Cd²⁺][OH⁻]²

As ksp = 2,5x10⁻¹⁴ and [OH⁻] at pH=12,30 = 10^-(14-12,30) = 0,01995M

2,5x10⁻¹⁴ = [Cd²⁺]×(0,01995M)²

[Cd²⁺] = 6,3x10⁻¹¹M

That means solubility is c. 6,3x10⁻¹¹M

I hope it helps!

D

Step-by-step explanation:

Multiply the numerator and denominator by the conjugate of the denominator.

Note that i² = - 1

The conjugate of 10 + 3i is 10 - 3i , then

← Expand numerator/denominator using FOIL

= ← simplify

=

= → D

D

Step-by-step explanation:

Multiply the numerator and denominator by the conjugate of the denominator.

Note that i² = - 1

The conjugate of 10 + 3i is 10 - 3i , then

← Expand numerator/denominator using FOIL

= ← simplify

=

= → D

Given:

The rate constant of the reaction, (K) = 2.3 × 10 -4 s-1

To find:

The half-life of a reaction.

Formula used:

The half-life of the reaction = 3.013 sec             (option A. is correct)